Answer:
$0.20
Step-by-step explanation:
4 x 1.45 = $5.80
6.00 - 5.80 = 0.20
Answer: $0.20
Step-by-step explanation:
Do 4 *$1.45 = $5.80
This is how much her total was.
She gave $6 in cash.
Subtract.
6-5.80=$.20
John used 1 3/4 kg os salt to melt the ice on the sidewalk. He then used another 3 4/5 kg on the driveway. How much salt did he use in all? PLEASE SHOW YOUR WORK I WILL MARK YOU BRAINIEST AND PLEASE EXPLAIN HOW YOU GOT YOUR WORK.
Answer:
111/20 = 5.55
Step-by-step explanation:
He used a total of 1 3/4 and 3 4/5 salt.
Convert both these mixed numbers into fractions.
=> 7/4 + 19/5
Take the LCM of the denominators
=> 35/20 + 76/20
Add the numerators
=> 111/20 = 5.55
He used a total of 111/20 or 5.55 kgs of salt.
for 0°<θ<-180° which of the primary trigonometric functions may have positive values?
sine and cosecant.
you can see the graph or on unit circle, as the for these ratios, (which depend on y coordinate) 1st and 2nd quadrant have positive y coordinate
Consider the equation: x 2 − 6 = 2 − 18 x x 2 −6=2−18xx, squared, minus, 6, equals, 2, minus, 18, x 1) Rewrite the equation by completing the square. Your equation should look like ( x + c ) 2 = d (x+c) 2 =dleft parenthesis, x, plus, c, right parenthesis, squared, equals, d or ( x − c ) 2 = d (x−c) 2 =dleft parenthesis, x, minus, c, right parenthesis, squared, equals, d. 2) What are the solutions to the equation? Choose 1 answer: Choose 1 answer: (Choice A) A x = 9 ± 89 x=9±89x, equals, 9, plus minus, 89 (Choice B) B x = − 9 ± 89 x=−9±89x, equals, minus, 9, plus minus, 89 (Choice C) C x = 9 ± 89 x=9± 89 x, equals, 9, plus minus, square root of, 89, end square root (Choice D) D x = − 9 ± 89 x=−9± 89 x, equals, minus, 9, plus minus, square root of, 89, end square root
Answer:
1. (x+9)^2 = 89
2. (Choice D) D x = − 9 ± 89 x=−9± 89 x, equals, minus, 9, plus minus, square root of, 89, end square root
Step-by-step explanation:
x^2 - 6 = 2 - 18x
1) rewrite the equation by completing the square
x^2 - 6 = 2 - 18x
x^2 + 18x = 2+6
x^2 + 18x = 8
Find the half of the coefficient of x and square it
18x
Half=9
Square half=(9)^2
=81
Add 81 to both sides
x^2 + 18x = 8
x^2 + 18x + 81 = 8 + 81
x^2 + 18x + 81 = 89
(x+9)^2 = 89
Check:
(x+9)(x+9)=89
x^2 + 9x + 9x + 81=89
x^2 + 18x +81 =89
2) (x+9)^2 = 89
√(x+9)^2 = √89
x+9=√89
x=√89 - 9
It can be rewritten as
x= -9 ± √89
(Choice D) D x = − 9 ± 89 x=−9± 89 x, equals, minus, 9, plus minus, square root of, 89, end square root
Compare the functions shown below: f(x) cosine graph with points at 0, negative 1 and pi over 2, 1 and pi, 3 and 3 pi over 2, 1 and 2 pi, negative 1 g(x) x y −6 −11 −5 −6 −4 −3 −3 −2 −2 −3 −1 −6 0 −11 h(x) = 2 cos x + 1 Which function has the greatest maximum y-value?
Answer:
f(x) and h(x) have the same maximum value: 3
Step-by-step explanation:
The maximum value of f(x) is 3 at (π, 3).
The maximum value of g(x) is -2 at (-3, -2).
The maximum value of h(x) is 3 at (0, 3).
Both f(x) and h(x) have the same (greatest) maximum value.
PLEASE - Select the correct answer.
Answer:
D
Step-by-step explanation:
-104=8x what is the answer?
Answer:
x=-12
Step-by-step explanation:
8x=-104
8x÷8=-104÷8
x=-104÷8
x=-13
Step-by-step explanation:
8x:-104
8÷8x:-104÷8
x:13
-10(x+5) with steps canvas
Answer:
[tex]\Large \boxed{-10x-50}[/tex]
Step-by-step explanation:
[tex]-10(x+5)[/tex]
Distribute -10 to the terms in the brackets.
[tex]-10(x)-10(5)[/tex]
[tex]-10x-50[/tex]
Answer: -10x - 50
Step-by-step explanation:
Distribute -10 to both terms.
-10 * x = -10x
-10 * 5 = -50
The equation now looks like this:
-10x - 50
You have nothing to simplify, so you're finished.
Hope this helps!
give area of a rectangle measuring 12 ft by 9ft and please show all the work
Answer:
Area= 108ft²
Step-by-step explanation:
To find the area of a rectangle, you must do the following formula:
Area= Length × Width
A represents Area
L represents Length
W represents Width
Because the length (length is always longer than width) is 12 ft and the width (width is always shorter than length) is 9 ft. Your equation should be:
A= L × W
= 12ft × 9ft
= 108 ft²
Remember: The answer to a question asking for the area of a shape that is 2D, is always squared (let x represents the answer: x²). And the question asking the area of a shape that is 3D always cubed (let x represents the answer: x³). Always write the unit of measurement (let x represent the answer and cm as the example of unit of measurement: x cm²)
I hope this helps! I'm sorry if it's too complicated.
Write the expression 12-2 in simplest form.
Answer:
convert into a whole number 6
A Gallup poll asked 1200 randomly chosen adults what they think the ideal number of children for a family is. Of this sample, 53% stated that they thought 2 children is the ideal number.
A Gallup poll asked 1200 randomly chosen adults what they think the ideal number of children for a family is. Of this sample, 53% stated that they thought 2 children is the ideal number. Construct and interpret a 95% confidence interval for the proportion of all US adults that think 2 children is the ideal number.
Answer:
at 95% Confidence interval level: 0.501776 < p < 0.558224
Step-by-step explanation:
sample size n = 1200
population proportion [tex]\hat p[/tex]= 53% - 0.53
At 95% confidence interval level;
level of significance ∝ = 1 - 0.95
level of significance ∝ = 0.05
The critical value for [tex]z_{\alpha/2} = z _{0.05/2}[/tex]
the critical value [tex]z _{0.025}= 1.96[/tex] from the standard normal z tables
The standard error S.E for the population proportion can be computed as follows:
[tex]S,E = \sqrt{\dfrac{\hat p \times (1-\hat p)}{n}}[/tex]
[tex]S,E = \sqrt{\dfrac{0.53 \times (1-0.53)}{1200}}[/tex]
[tex]S,E = \sqrt{\dfrac{0.53 \times (0.47)}{1200}}[/tex]
[tex]S,E = \sqrt{\dfrac{0.2491}{1200}}[/tex]
[tex]S,E = 0.0144[/tex]
Margin of Error E= [tex]z_{\alpha/2} \times S.E[/tex]
Margin of Error E= 1.96 × 0.0144
Margin of Error E= 0.028224
Given that the confidence interval for the proportion is 95%
The lower and the upper limit for this study is as follows:
Lower limit: [tex]\hat p - E[/tex]
Lower limit: 0.53 - 0.028224
Lower limit: 0.501776
Upper limit: [tex]\hat p + E[/tex]
Upper limit: 0.53 + 0.028224
Upper limit: 0.558224
Therefore at 95% Confidence interval level: 0.501776 < p < 0.558224
The circle shown above has a radius of 5 units, and the central angle of the sector that is shaded is 25π radians. Determine the area of the shaded sector, in terms of π. Enter the area of the sector.
Answer:
The answer is below
Step-by-step explanation:
Given that:
The radius of the circle (r) = 5 units
The central angle (θ) = 25π
A sector of a circle is the portion of a circle made up of two of its radii and an arc. The area of a sector that subtends with a central angle (θ) and a radius (r) is given by the formula:
[tex]Area\ of\ sector=\frac{\theta}{360} *\pi r^2[/tex]
Substituting the radius of the circle and the central angle:
[tex]Area\ of\ sector=\frac{\theta}{360} *\pi r^2\\\\Area\ of\ sector=\frac{25\pi}{360} *\pi (5)^2\\\\Area\ of\ sector=\frac{125\pi^2}{72}[/tex]
2. The fraction 84 by 98 in simplest form is
Answer: 6/7
Step-by-step explanation: Since the Greatest common factor of 84 and 98 is 14, you divide both sides of 84/98 by 14 to get 6/7
Answer:6/7
Step-by-step explanation:The greatest common factor of both numerator and denominator is 14.So if you divide 84 by 14 you will get 6 and if you divide 98 by 14 you get 7.
Soda Tak claims that Diet Tak has 40mg of sodium per can. You work for a consumer organization that tests such claims. You take a random sample of 60 cans and find that the mean amount of sodium in the sample is 41.9mg. The population standard deviation in all cans is 5.2mg. You suspect that there is more than 40mg of sodium per can. Find the z-score.
Answer:
Z - score = 2.83
Step-by-step explanation:
Given the following :
Number of samples (N) = 60
Sample mean (x) = 41.9mg
Population mean (μ) = 40mg
Population standard deviation (sd) = 5.2
Using the relation :
Z = (x - μ) / (sd / √N)
Z = (41.9 - 40) / (5.2 / √60)
Z = 1.9 / (5.2 / 7.7459666)
Z = 1.9 / 0.6713171
Z = 2.8302570
Therefore, the z-score = 2.83
Find the next three terms in the geometric sequence.
Answer: D
Step-by-step explanation:
The common difference is -2/3 so using the last term which is -8/27 multiply it by -2/3 to find the next terms.
[tex]-\frac{8}{27} * -\frac{2}{3}[/tex] = [tex]\frac{16}{81}[/tex]
[tex]\frac{16}{81} * -\frac{2}{3} = -\frac{31}{243}[/tex]
[tex]-\frac{32}{243} * -\frac{2}{3} = \frac{64}{729}[/tex]
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. The height (in feet) of a rocket launched from the ground is given by the function f(t) = -16t2 + 160t. Match each value of time elapsed (in seconds) after the rocket’s launch to the rocket's corresponding instantaneous velocity (in feet/second).
Answer:
The pairs are;
t, v
2, 96
4, 32
5, 0
6, -32
7, -64
9, -128
Step-by-step explanation:
The given equation is f(t) = -16·t² + 160·t
We have, the velocity, v = d(f(t))/dt = d(-16·t² + 160·t)/dt = -32·t + 160
Which gives;
t, v
0, -32×(0) + 160 = 160
1, -32×(1) + 160 = 128
2, -32×(2) + 160 = 96
3, -32×(3) + 160 = 64
4, -32×(4) + 160 = 32
5, -32×(5) + 160 = 0
6, -32×(6) + 160 = -32
7, -32×(7) + 160 = -64
8, -32×(8) + 160 = -96
9, -32×(9) + 160 = -128
The given velocity values are;
96, -64, 32, 0, -128, -32 which correspond to 2, 7, 4, 5, 9, 6
The pairs are;
t, v
2, 96
4, 32
5, 0
6, -32
7, -64
9, -128
The average annual amount American households spend for daily transportation is $6312 (Money, August 2001). Assume that the amount spent is normally distributed.a. Suppose you learn that 5% of American households spend less than $1000 for dailytransportation. What is the standard deviation of the amount spent?b. What is the probability that a household spends between $4000 and $6000?c. What is the range of spending for the 3% of households with the highest daily transportationcost?
Answer:
(a) The standard deviation of the amount spent is $3229.18.
(b) The probability that a household spends between $4000 and $6000 is 0.2283.
(c) The range of spending for 3% of households with the highest daily transportation cost is $12382.86 or more.
Step-by-step explanation:
We are given that the average annual amount American households spend on daily transportation is $6312 (Money, August 2001). Assume that the amount spent is normally distributed.
(a) It is stated that 5% of American households spend less than $1000 for daily transportation.
Let X = the amount spent on daily transportation
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = average annual amount American households spend on daily transportation = $6,312
[tex]\sigma[/tex] = standard deviation
Now, 5% of American households spend less than $1000 on daily transportation means that;
P(X < $1,000) = 0.05
P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{\$1000-\$6312}{\sigma}[/tex] ) = 0.05
P(Z < [tex]\frac{\$1000-\$6312}{\sigma}[/tex] ) = 0.05
In the z-table, the critical value of z which represents the area of below 5% is given as -1.645, this means;
[tex]\frac{\$1000-\$6312}{\sigma}=-1.645[/tex]
[tex]\sigma=\frac{-\$5312}{-1.645}[/tex] = 3229.18
So, the standard deviation of the amount spent is $3229.18.
(b) The probability that a household spends between $4000 and $6000 is given by = P($4000 < X < $6000)
P($4000 < X < $6000) = P(X < $6000) - P(X [tex]\leq[/tex] $4000)
P(X < $6000) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{\$6000-\$6312}{\$3229.18}[/tex] ) = P(Z < -0.09) = 1 - P(Z [tex]\leq[/tex] 0.09)
= 1 - 0.5359 = 0.4641
P(X [tex]\leq[/tex] $4000) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{\$4000-\$6312}{\$3229.18}[/tex] ) = P(Z [tex]\leq[/tex] -0.72) = 1 - P(Z < 0.72)
= 1 - 0.7642 = 0.2358
Therefore, P($4000 < X < $6000) = 0.4641 - 0.2358 = 0.2283.
(c) The range of spending for 3% of households with the highest daily transportation cost is given by;
P(X > x) = 0.03 {where x is the required range}
P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{x-\$6312}{3229.18}[/tex] ) = 0.03
P(Z > [tex]\frac{x-\$6312}{3229.18}[/tex] ) = 0.03
In the z-table, the critical value of z which represents the area of top 3% is given as 1.88, this means;
[tex]\frac{x-\$6312}{3229.18}=1.88[/tex]
[tex]{x-\$6312}=1.88\times 3229.18[/tex]
x = $6312 + 6070.86 = $12382.86
So, the range of spending for 3% of households with the highest daily transportation cost is $12382.86 or more.
What is the image point of (-5,9) after a translation left 1 unit and down 1 unit?
Answer: (-6,8)
Step-by-step explanation:
Translation is a rigid motion inn which every point of the figure moved in the same direction and for the same distanceTranslation rules are
Left c units : [tex](x,y)\to(x-c,y)[/tex]
Down c units : [tex](x,y)\to(x,y-c)[/tex]
The image point of (-5,9) after a translation left 1 unit and down 1 unit will be:
[tex](-5,9)\to(-5-1,9-1)=(-6,8)[/tex]
Hence, the image point is (-6,8).
i need help with this question
Answer:
1000ml
Step-by-step explanation:
4 days she drank ½ of the bottle
so she drank ⅛ l of juice everyday
so
1000ml is the answer
a rectangle is 12 in wide and 18 in tall.if it is reduce to a height of 3 inches, then how wide will it be?
Answer:
2 in
Step-by-step explanation:
18/3=6 , 6 is the scale factor
12/6=2
Answer:
width= 2
Step-by-step explanation:
18 inches is the original height and we are now reducing that to 3 inches.
In order to do that, we have to divide 18 by 3 which equals 6.
Next, take the width of the rectangle, which is twelve and divide it by the scale factor of 6 which equals 2.
Your final answers should be: width= 2
Evaluate without actual multiplication 1) 95x96 2)103x107
Answer:
:
"(100 + 3) (100 + 7)
Now, by using identity
(x + a) (x + b) = x² + (a+b)*x + ab
So,
x = 100 , a = 3 , b = 7
= (100)² + (3+7)*100 + (3*7)
= 10000 + 1000 + 21
= 11021
.
(110 - 7) (110 - 3)
by using identity
(x + a) (x + b) = x² + (a+b)*x + ab
So,
x = 100 , a = (-7) , b = (-3)
= (110)² + { (-7) + (-3) }*110 + {(-7)*(-3)}
= 12100 + (-10)*110 + 21
= 21200 - 1100 + 21
= 11021
.
➖➖➖➖➖➖➖➖➖➖
.
(90 + 5) (90 + 6)
by using identity
(x + a) (x + b) = x² + (a+b)*x + ab
So,
x = 90 , a = 5 , b = 6
= (90)² + (5+6)*90 + (5*6)
= 8100 + 990 + 30
= 9120
.
(100 - 5) (100 - 4)
by using identity
(x + a) (x + b) = x² + (a+b)*x + ab
So,
x = 100 , a = (-5) , b = (-4)
= (100)² + { (-5) + (-4) }*100 + 20
= 10000 + (-9)*100 + 20
= 10000 - 9000 + 20
= 10020 - 900
= 9120
.
➖➖➖➖➖➖➖➖➖➖
.
(100 + 4) (100 - 4)
by using identity
(x + a) (x + b) = x² + (a+b)*x + ab
So,
x = 100 , a = 4 , b = (-4)
= (100)² + { 4 + (-4) }*100 + 4*(-4)
= 10000 + (4 - 4)*100 - 16
= 10000 + 0*100 - 16
= 10000 - 16
= 9984
.
(90 + 14) (90 + 6)
by using identity
(x + a) (x + b) = x² + (a+b)*x + ab
So,
x = 90 , a = 14 , b = 6
= (90)² + (14 + 6)*90 + (14*6)
= 8100 + 20*90 + 84
= 8100 + 1800 + 84
= 9984"
This answer was in another question
This answer was given by BloomingBud
Step-by-step explanation:
Answer:
1) 9120 2) 11021
Step-by-step explanation:
95 * 96 = (100-5)(100-4) = 10000 - 500 - 400 + 20 = 9120
103 * 107 = (100+3)(100+7) = 10000 + 300 + 700 + 21 = 11021
I need helpp!! match the building block of geometry to the statement that defines it.
1)DIAGRAM
A)a formal statement declaring the meaning of
a word
2)DEFINITION
B)a visual tool representing mathematical
ideas to be interpreted
3)THEOREM
C)a mathematical statement proven using
postulates and definitions
4)POSTULATE
D)a mathematical statement taken as a fact
Answer:
1) [tex]DIAGRAM \mapsto B[/tex]
2) DEFINITION [tex]\mapsto A[/tex]
3) THEOREM [tex]\mapsto C[/tex]
4) POSTULATE [tex]\mapsto D[/tex]
Step-by-step explanation:
1) DIAGRAM B) A visual tool representing mathematical ideas to be interpreted
A diagram is the depiction or representation of information using symbols
2) DEFINITION A) A formal statement declaring the meaning of a word
A definition is a statement that outlines the meaning of a word or a group of words or a diagram, or a symbol or sign
3) THEOREM C) A mathematical statement proven using postulates and definitions
A general statement of a proposition that is by itself not evident, but given proof by a combination of postulates
4) POSTULATE D) A mathematical statement taken as a fact
An assumed truth taken as the foundation for further reasoning
PLEASE ANSWER QUICKLY ASAP
ANSWER QUESTION A AND B
Answer:
a) [tex]a+b+c=\begin{pmatrix}-2\\-3\end{pmatrix}[/tex]
b) (i) [tex]a+2c=\begin{pmatrix}-4\\2\end{pmatrix}[/tex]
(ii) [tex]k=2[/tex]
Step-by-step explanation:
It is given that,
[tex]a=\begin{pmatrix}4\\-10\end{pmatrix},b=\begin{pmatrix}-2\\1\end{pmatrix},c=\begin{pmatrix}-4\\6\end{pmatrix}[/tex]
a)
We need to find the value of a+b+c.
[tex]a+b+c=\begin{pmatrix}4\\-10\end{pmatrix}+\begin{pmatrix}-2\\1\end{pmatrix}+\begin{pmatrix}-4\\6\end{pmatrix}[/tex]
[tex]a+b+c=\begin{pmatrix}4+(-2)+(-4)\\-10+1+6\end{pmatrix}[/tex]
[tex]a+b+c=\begin{pmatrix}-2\\-3\end{pmatrix}[/tex]
b)
(i) We need to find the value of a+2c.
[tex]a+2c=\begin{pmatrix}4\\-10\end{pmatrix}+2\begin{pmatrix}-4\\6\end{pmatrix}[/tex]
[tex]a+2c=\begin{pmatrix}4\\-10\end{pmatrix}+\begin{pmatrix}-8\\12\end{pmatrix}[/tex]
[tex]a+2c=\begin{pmatrix}4+(-8)\\-10+12\end{pmatrix}[/tex]
[tex]a+2c=\begin{pmatrix}-4\\2\end{pmatrix}[/tex]
(ii) It is given that a+2c=kb, where k is an integer. We need to find the value of k.
[tex]a+2c=k\begin{pmatrix}-2\\1\end{pmatrix}[/tex]
[tex]\begin{pmatrix}-4\\2\end{pmatrix}=\begin{pmatrix}-2k\\k\end{pmatrix}[/tex]
On comparing both sides, we get
[tex]k=2[/tex]
Triangle P Q R is shown. The length of P Q is 17, the length of Q R is 15, and the length of P R is 14. Law of cosines: a2 = b2 + c2 – 2bccos(A) What is the measure of AngleP to the nearest whole degree? 35° 52° 57° 72°
Answer:
P = 57°
Step-by-step explanation:
Given the following :
PQ = 17
QR = 15
PR = 14
Using the cosine formula since the length of the three sides are given:
a2 = b2 + c2 – 2bccos(A)
To find P:
QR^2 = PQ^2 + PR^2 – 2(PQ)(PR)cos(P)
15^2 = 17^2 + 14^2 – 2(17)(14)cos(P)
225 = 289 + 196 - 476 cosP
476*CosP = 485 - 225
476*CosP = 260
CosP = 260/476
CosP = 0.5462184
P = Cos^-1(0.5462184)
P = 56.892029
P = 57°
Answer:
57 degrees
Step-by-step explanation:
just took the test on edg2020
1. At the end of one school day a teacher had 17 crayons left. The teacher remembered
giving out 14 crayons in the morning, getting 12 crayons back at recess, and giving out
11 crayons after lunch. How many crayons did the teacher have at the start of the
day?
Answer:
30 crayons
Step-by-step explanation:
Let x be the number of crayons he started with
gave out 14 crayons
x-14
Got 12 back
x-14+12
Gave out 11 after lunch
x-14+12 -11
This equals 17
x-14+12 -11 =17
Combine like terms
x-13 = 17
Add 13 to each side
x -13+13 =17+13
x = 30
Answer: 30
Step-by-step explanation:
For this problem work backwards. Start from 17 and add 14. You should get 31. Then subtract 12, which equals 19. Finally add 11 to 19, which equals 30. Basically you are doing the inverse operation to get your answer. Hope this helps!
anyone know how to solve a functions equation such as x^2-x-x <0
Answer:
Step-by-step explanation:
[tex]x^{2} -x-x<[/tex] 0
[tex]x^{2} -2x[/tex] < 0
x^2-2x+1<1
(x-1）^2<1
-1<x-1<1
0<x<2
[tex](x-1)^{2}[/tex][tex](x-1)^{2}[/tex]
is 1 whole 1 by 3 considered as an integer??
Answer:
No it's not.
Step-by-step explanation:
[tex]1 \frac{1}{3} = \frac{4}{3} = 1.333333[/tex]
Integers are set of numbers consisting
Whole numberNatural numberNegative numbersIt doesn't consist
Fractions &DecimalsHope this helps ;) ❤❤❤
Answer:
[tex]\boxed{\sf No}[/tex]
Step-by-step explanation:
[tex]\displaystyle 1 \frac{1}{3} =1.3333333...[/tex]
Integers are whole numbers that can be positive or negative. Integers do not include fractions and decimals.
Given that ΔABC is a right triangle with the right angle at C, which of the following is true?
1. tan A = 1/(tan B)
2. tan A = sin B
3. cos A = 1/(cos B)
4. sin B = 1/(sin A)
Answer:
1. tan A = 1/(tan B)
Step-by-step explanation:
By definition,
tangent A = opposite / adjacent = a / b
and
tangent B = opposite / adjacent = b / a
Therefore tangent A = a/b = 1/tan(B)
Answer: Tan a=tan b
I belive
Step-by-step explanation:
For what real numbers x is x 2 − 10 x + 25 negative?
Answer:
no real numbers
Step-by-step explanation:
x^2 − 10 x + 25
Factor
What 2 numbers multiply to 25 and add to -10
-5*-5 = 25
-5+-5 = -10
( x-5) (x-5)
This touches the graph at x =5
The parabola is positive so there are no values where the graph is negative
Answer:
No real solutions
Step-by-step explanation:
Part 1: Factoring the quadratic
The equation is in quadratic form - ax² + bx + c = 0.
Therefore, we can use a factoring technique to solve for x. I will use the quadratic formula - [tex]x=\frac{-b \pm \sqrt{b^{2}-4ac} }{2a}[/tex].
[tex]x=\frac{-(-10)\pm \sqrt{(-10)^{2}-4(1)(25)} }{2(1)}\\\\x=\frac{10\pm\sqrt{100-4(25)} }{2}\\\\x=\frac{10\pm\sqrt{100-100}}{2}\\\\x=\frac{10\pm\sqrt{0}}{2}\\\\x=\frac{10\pm0}{2}\\\\x=\frac{10}{2}\\\\\boxed{x=5}[/tex]
Part 2: Using discriminant to determine roots
Because the discriminant (square root portion of formula) was equivalent to zero, this is the only solution that proves the equation correctly. Therefore, there is no possible negative value that can be substituted for x without altering the final value that the equation is equal to.
You and your best friend are both on the swim team. You want to beat your friend at the next swim meet so you decide to swim 151515 minutes longer than she does one day at practice. Write an equation for the number of minutes you swim, yyy, when your friend swims xxx number of minutes.
Answer:
y = x + 15
Step-by-step explanation:
My friend swims x minutes.
I swim 15 minutes more than my friends, so I swim x + 15 minutes.
I swim y minutes, so y equals x + 15
Answer: y = x + 15
6=m/8 whats does m equal?
Answer:
m=48
Step-by-step explanation:
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▹ Answer
m = 48
▹ Step-by-Step Explanation
Rewrite:
m/8 = 6
Use the inverse operation:
8 * 6 = 48
m = 48
Hope this helps!
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